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Title:
Representation Theory and Gauge Theory
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Abstract:
The gauge theory is a quantum field theory based on the theory of connections on principal bundles over the space-time. The Lie group appears as a structure group of principal bundles. In particular, the representation theory of Lie groups has been used in the gauge theory as a language. In the last few decades, much deeper links between gauge theory and representation theory have been developed. Not only local symmetry of the gauge theory is controlled by a Lie group, more global structures of the theory can be understood by representation theory of a Lie group or a related algebra, which is usually different from the original one. I will explain that the W-algebra (a generalization of Virasoro algebra) appears two seemingly unrelated gauge theories in 2d and 4d (the AGT
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